Generating singularities of solutions of quasilinear elliptic equations using Wolff’s potential

Title:

Generating singularities of solutions of quasilinear elliptic equations using Wolff’s potential

Creator:

Žubrinić, Darko

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:29794995-c34a-4b1e-be62-b4d248db214e
uuid:29794995-c34a-4b1e-be62-b4d248db214e

Subject:

quasilinear elliptic, singularity, and Sobolev function

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We consider a quasilinear elliptic problem whose left-hand side is a Leray-Lions operator of $p$-Laplacian type. If $p<\gamma <N$ and the right-hand side is a Radon measure with singularity of order $\gamma $ at $x_0\in \Omega $, then any supersolution in $W_{\mathrm loc}^{1,p}(\Omega )$ has singularity of order at least $\frac{(\gamma -p)}{(p-1)}$ at $x_0$. In the proof we exploit a pointwise estimate of $\mathcal A$-superharmonic solutions, due to Kilpeläinen and Malý, which involves Wolff’s potential of Radon’s measure.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

429-435

Source:

Czechoslovak Mathematical Journal | 2003 Volume:53 | Number:2

Harvested from:

CDK

Metadata only:

false